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On relationship between canonical momentum and geometric momentum
- Publication Year :
- 2016
-
Abstract
- Decompositing of $N+1$-dimensional gradient operator in terms of Gaussian normal coordinates $(\xi^{0},\xi^{\mu})$, ($\mu=1,2,3,...,N$) and making the canonical momentum $P_{0}$ along the normal direction $\mathbf{n}$ to be hermitian, we obtain $\mathbf{n}P_{0}=-i\hbar\left( \mathbf{n}\partial _{0}-\mathbf{M}_{0}\right) $ with $\mathbf{M}_{0}$ denoting the mean curvature vector on the surface $\xi^{0}=const.$ The remaining part of the momentum operator lies on the surface, which is identical to the geometric one.<br />Comment: 7 pages
- Subjects :
- Quantum Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1605.01597
- Document Type :
- Working Paper